Magnetic disk devices are used in a very wide variety of fields, and development continues to realize more compact and higher density devices. To further increase the density, it is necessary to reduce the gap (i.e., the flying height of the magnetic head) between the magnetic head and the magnetic disk in the R/W gap portion from 0.2 .mu.m (currently available) to 0.1 .mu.m. To this end, it is important to measure the flying height (about 0.1 .mu.m) of manufactured magnetic heads to test whether they can fly as designed.
There is a previously known method of measuring the flying height in which an unknown gap (flying height) is determined by illuminating a magnetic head that is flying above a transparent quartz disk by shining white light through the disk, and comparing the spectral line shape of the interference color caused by the gap between the magnetic head and the quartz disk with the theoretical value (See "Automatic Digital Flying Tester" in a catalog published by Pacific Precision Laboratories, Inc., 1988).
With reference to FIG. 1, the principle of optically measuring the flying height is described below. FIG. 1 shows a state in which a transparent quartz disk 1 and a magnetic head 3 that is flying are separated by a distance d. Light 4 from the quartz disk 1 reaching an air gap 2 at an incident angle .theta..sub.1 is refracted to enter the air gap 2 at a refraction angle .theta..sub.2, and made incident on the head 3 at an incident angle .theta..sub.2 that is equal to the above refraction angle. One part 5 of the light enters the head 3 at an angle .theta..sub.3 and is absorbed therein. The remaining part of the light is reflected by the head 3, and is then divided into light 7 that is again reflected by the surface of the quartz disk 1 and light 6 that enters the quartz disk 1. Through this multiple reflection, the intensity of the light that includes beams having different optical paths is modulated by the interference effect.
Taking this effect into account, the reflection coefficient r of the light 6 output from the quartz disk 1 is expressed by the following equation if the incident light is an S wave (Pochi Yeh, "Optical Waves in Layered Media," A Wiley-Interscience Publication, John Wiley and Sons, 1988, New York): ##EQU1##
In the above equations, n.sub.1, n.sub.2, and n.sub.3 represent the complex refractive indices of the quartz disk 1, air, and magnetic head 3, respectively; .lambda., the wavelength of the incident light; d, the air gap, that is, the flying height; c, the speed of light; and .omega., the angular frequency of the incident light. Further, r.sub.12 represents the reflection coefficient at the interface between the disk 1 and the air gap 2; r.sub.23, the reflection coefficient at the interface between the air gap 2 and the magnetic head 3; and k.sub.i, the i-component of the wave propagation vector.
Since the quartz disk 1 and air have little absorption loss, their refractive indices n.sub.1 and n.sub.2 are real numbers. However, the refractive index n.sub.3 is a complex number. Therefore, from Eqs. (3) and (4), r.sub.23 is a complex number, and is expressed by EQU r.sub.23 =-.vertline.r.sub.23 .vertline.Exp(i.phi.) (.phi.&gt;0) (6)
In general, .vertline.r.sub.23 .vertline. and .phi. are functions of .lambda.. Using these parameters, Eq. (1) can be written, using only real numbers, as ##EQU2##
At this time, it should be considered that what is actually measurable is the reflectance R, rather than the reflection coefficient r. The reflectance R is expressed by ##EQU3## where EQU R.sub.12 =r.sub.12.sup.2 ( 10) EQU R.sub.23 =.vertline.r.sub.23 .vertline..sup.2 ( 11)
The reflected light intensity is a product of the intensity of the incident light and the coefficient R. Therefore, Eq. (9) represents, without a scaling factor, the reflected light intensity when light having a certain wavelength .lambda. is incident on a gap d at an incident angle .theta..sub.1.
The value of the complex refractive index n.sub.3 of the magnetic head 3 differs according to the material and the laminated structure of the head 3 as well as the coating method. However, since n.sub.3 takes a fixed, specific value once the structure, material, and so on have been determined, it can be obtained by dividing n.sub.3 into a real part (refractive index) and an imaginary part (extinction coefficient), and calculating each of these parts as parameters when fitting a theoretical equation (Eq. (9) or a modification thereof) into measurement data.
FIGS. 2-4 are examples of the wavelength dependence of the intensity R of the light reflected to the quartz disk 1, which were calculated by using Eq. (9). The wavelength range is 350-800 nm, and the incident angle is 0 degree. The flying heights (air gaps) d are indicated in the graphs as parameters. It can be seen that the spectral line shape varies with the flying height.
Conventional methods for measuring flying height utilize the above white light interference effect occurring at the air gap. That is, the variation, with the distance d, of the interference color of the white light incident on the magnetic head flying above the transparent quartz disk is determined in advance by measuring its spectrum through the use of a diffraction grating, and the actual distance d of the magnetic head is calculated from the spectral line shape. However, as is apparent from FIG. 2, in a small flying height range (80-120 nm), the reflected light intensity varies monotonically with the wavelength. Particularly when a lamp, such as a tungsten lamp having low brightness in a short wavelength range is used, a spectral variation is hardly detected even when the flying height is varied. Therefore, it can be said that the methods conventionally used widely are not suitable for the evaluation of magnetic heads having a small flying height, which will form the majority of those used in future magnetic disks. Furthermore, a very bright light source needs to be employed to compensate for the light intensity reduction that occurs when the light is separated into its spectral components. This increases the price of the measurement apparatus used with such optical devices as a diffraction grating.
To avoid the above problems, other methods have been proposed in which light beams of two wavelengths are employed as probing light beams. For example, in PUPA No. 1-260305, an He-Ne laser (633 nm) and a semiconductor laser (830 nm) are employed as two kinds of light source. To estimate the flying height of the head, the reflected light intensity is measured for the respective wavelengths and the measured values are plotted on a curve for the respective wavelengths, correlating the reflected light intensity and the disk-head gap (output function of a photodetector). However, the actual comparison of the measured values and the correlation curves is performed by using two tables stored in a ROM, each describing the relationship between the reflected light intensity and the flying height. Consequently, the flying height cannot be determined correctly because of the global decision error (described later).
The least-square method can be easily applied to the above method of using two-color laser beams as a technique for comparing measured values with the output function of a photodetector. However, this combination has the following associated problems.
FIG. 5 shows two curves representing the relationship of the gap (flying height) d separating the magnetic head and the quartz disk and the intensity of the reflected light input from the quartz disk, which have been calculated and plotted for the two wavelengths, 633 nm (indicated by (A)) and 830 nm (indicated by (B)). These two functions are represented by F.sub.633 (d) and F.sub.830 (d), respectively.
A description is now given of how an experimenter estimates the flying height d on the assumption that the true value of d is 58 nm. There is a gap dependency of the sum of the squares of the respective differences between the two measured reflected light intensities, .sup.633 R.sub.58 and .sup.830 R.sub.58, and the corresponding values on the characteristic curves F.sub.633 (d) and F.sub.830 (d) in FIG. 5. ##EQU4##
The minimum of the left side of this equation gives the flying height d. However, it may be that the function Es(d) has a local minimum in addition to the true minimum that gives the flying height d. If this kind of local minimum is located within the range of measurement errors, a false flying height, rather than the true one, may be given. This type of error is called a global decision error.
In FIG. 6, the minimum Lm(d) of the local minima of functions Es(d) are plotted for various gaps. There exist values of the gap interval d that are associated either with no local minimum within the range of FIG. 6 or with a plurality of local minima. FIG. 6 shows all the local minima obtained when d is varied at intervals of 1 nm.
While the minimum of Es(d) gives the true gap itself, that is, the flying height itself, Lm(d) is a local minimum other than the minimum of Es(d) and therefore does not correspond to the true gap. If the local minimum is located within the range of measurement error, it may give a false flying height. In other words, the difference between Lm(d) and the zero level can be regarded as the margin of measurement error.
When the two wavelengths of the semiconductor laser and the He-Ne laser are used, the measurement error is about 0.005 in noise level as shown in FIG. 6. Therefore, when the gap interval length is changed between 50 nm and 900 nm, the margin of error is actually entirely contained in the measurement error in most areas. Thus, the true flying height cannot be obtained.
Further, the method for generating two-color laser beams by using separate light sources needs an optical system to collimate the two beams into a single beam. Where a semiconductor laser is used, a lens system is needed to compensate for the difference in the aspect ratio of the semiconductor laser beam.
Furthermore, conventionally, the least-square calculation for estimating the flying height is performed by an off-line-type algorithm. Therefore, when the least-square method is applied to the method of optically determining the flying height, it is very difficult to automate the measurement or measure the dynamics of the flying height of the head.
Therefore, what is needed is an apparatus for measuring the head's flying height that has high sensitivity and a simple constitution. The apparatus should also use real-time, least-square calculation for estimating the flying height of the head.